A basic idea in all pattern discovery methods is to model statistical regularities and to compare a model to an actual representation in order to measure a similarity or similarities between the created (learned) model and a present pattern under analysis.
One of known methods and techniques utilised for modeling and recognizing patterns in sequences is the Markov model, which assumes that a sequence to be modelled has the Markov property. Having the Markov property means that, given a present state, future states are independent of past states. In other words, the description of the present state alone fully captures all information that could influence the future evolution of the process. The future states will be reached through a probabilistic process instead of a deterministic process.
At each step a system may change its state from the present state to another state, or remain in the same state, according to a certain probability distribution. The changes of the state are called transitions, and the probabilities associated with various state changes are called transition probabilities.
Many physical processes and corresponding observable sequences, which are created by the physical processes, have strong structures such as temporal structures which can be measured by higher order correlation coefficients. Thus, depending on the temporal resolution used the created sequence may have wide structures (over time or space), which cannot be modeled accurately by a Markov chain where future states are independent of the past states.